• RAM NIWAS MEGHWAL
• DR.K.G. BHADANA

A large number of fractional derivative and Eulerian integral formulae of multivariable H- Function containing general class of polynomial have been presented. Here, in this paper, our aim is to establishing three fractional integral formulas involving the products of the multivariable H-function and a general class of polynomials by using generalized fractional integration operators given by Saigo and Maeda [M. Saigo, N. Maeda, Varna, Bulgaria, (1996), 386–400]. All the results derived here being of general character, they are seen to yield a number of results (known and new) regarding fractional integrals.In this paper we use fractional differential operators and to derive a number of key formulas of multivariable H-function. We use the generalized Leibnitz’s rule for fractional derivatives in order to obtain one of the aforementioned formulas, which involve a product of two multivariable’s H-function. It is further shown that ,each of these formulas yield interesting new formulas for certain multivariable hypergeometric function such as generalized Lauricella function (Srivastava-Dauost)and Lauriella hypergeometric function some of these application of the key formulas provide potentially useful generalization of known result in the theory of fractional calculus.

"Solution of fractional derivative and Eulerian integral formulae of multivariable H- Function containing general class of polynomial", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 4, page no.f433-f441, April-2024, Available :http://www.jetir.org/papers/JETIR2404547.pdf

"Solution of fractional derivative and Eulerian integral formulae of multivariable H- Function containing general class of polynomial", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 4, page no. ppf433-f441, April-2024, Available at : http://www.jetir.org/papers/JETIR2404547.pdf